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A High-Order Method for Stiff Boundary Value Problems with Turning Points

Brown, David L. and Lorenz, Jens (1987) A High-Order Method for Stiff Boundary Value Problems with Turning Points. SIAM Journal on Scientific and Statistical Computing, 8 (5). pp. 790-805. ISSN 0196-5204. doi:10.1137/0908067.

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This paper describes some high-order collocation-like methods for the numerical solution of stiff boundary-value problems with turning points. The presentation concentrates on the implementation of these methods in conjunction with the implementation of the a priori mesh construction algorithm introduced by Kreiss, Nichols and Brown [SIAM J. Numer. Anal., 23 (1986), pp. 325–368] for such problems. Numerical examples are given showing the high accuracy which can be obtained in solving the boundary value problem for singularly perturbed ordinary differential equations with turning points.

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Additional Information:© 1987 Society for Industrial and Applied Mathematics. Received January 13, 1986; accepted (in revised form) September 29, 1986; Published online: 14 July 2006. This research was supported in part by National Science Foundation grant DMS-8312264 and Department of Energy grant DE/AT03/76ER/72012. Part of the computer time used for the code development described in this paper was provided by IBM on an IBM 4341 at the California Institute of Technology. We would like to thank Heinz Kreiss for many valuable discussions.
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Department of Energy (DOE)DE-AT03-76ER-72012
Subject Keywords:stiff boundary value problems; turning points; collocation; mesh construction
Issue or Number:5
Classification Code:AMS Subject Headings: 34A50; 34B05; 34E20; 65L10; 65L50
Record Number:CaltechAUTHORS:20120626-164218625
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Official Citation:A High-Order Method for Stiff Boundary Value Problems with Turning Points Brown, D. and Lorenz, J. SIAM Journal on Scientific and Statistical Computing 1987 8:5, 790-805
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:32113
Deposited On:27 Jun 2012 14:22
Last Modified:09 Nov 2021 21:15

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